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A073379 Ninth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.

%I A073379 #17 Aug 20 2024 23:16:55
%S A073379 1,10,75,440,2255,10362,43945,174460,656370,2359500,8158722,27275040,
%T A073379 88524930,279892380,864508590,2614740216,7759693095,22634343270,
%U A073379 64990287285,183929970840,513661549401,1416970676550
%N A073379 Ninth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.
%C A073379 For a(n) in terms of U(n+1) and U(n), with U(n) = A001045(n+1), see A073370 and the row polynomials of triangles A073399 and A073400.
%H A073379 G. C. Greubel, <a href="/A073379/b073379.txt">Table of n, a(n) for n = 0..1000</a>
%H A073379 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (10,-25,-60,330,12,-1770,960,5835,-4070,-13597, 8140,23340,-7680,-28320,-384,21120,7680,-6400,-5120,-1024).
%F A073379 a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073378(k).
%F A073379 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+9, 9) * binomial(n-k, k) * 2^k.
%F A073379 G.f.: 1/(1-(1+2*x)*x)^10 = 1/((1+x)*(1-2*x))^10.
%t A073379 CoefficientList[Series[1/((1+x)*(1-2*x))^10, {x,0,40}], x] (* _G. C. Greubel_, Oct 01 2022 *)
%o A073379 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^10 )); // _G. C. Greubel_, Oct 01 2022
%o A073379 (SageMath)
%o A073379 def A073379_list(prec):
%o A073379     P.<x> = PowerSeriesRing(ZZ, prec)
%o A073379     return P( 1/((1+x)*(1-2*x))^10 ).list()
%o A073379 A073379_list(40) # _G. C. Greubel_, Oct 01 2022
%Y A073379 Tenth (m=9) column of triangle A073370.
%Y A073379 Cf. A001045, A073370, A073378, A073399, A073400.
%K A073379 nonn,easy
%O A073379 0,2
%A A073379 _Wolfdieter Lang_, Aug 02 2002